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प्रश्न
Find the mid-point of the line segment joining the points:
(5, –3) and (–1, 7)
उत्तर
A(5, –3) and B(–1, 7)
Mid-point of AB = `((5 - 1)/2, (-3 + 7)/2)`
= (2, 2)
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संबंधित प्रश्न
P(–3, 2) is the mid-point of line segment AB as shown in the given figure. Find the co-ordinates of points A and B.
Points A(–5, x), B(y, 7) and C(1, –3) are collinear (i.e. lie on the same straight line) such that AB = BC. Calculate the values of x and y.
A(5, x), B(−4, 3) and C(y, –2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y.
Find th co-ordinates of the midpoint of the line segment joining P(0, 6) and Q(12, 20).
Find the midpoint of the line segment joining the following pair of point :
( -3, 5) and (9, -9)
A(6, -2), B(3, -2) and C(S, 6) are the three vertices of a parallelogram ABCD. Find the coordinates of the fourth vertex c.
Let A(-a, 0), B(0, a) and C(α , β) be the vertices of the L1 ABC and G be its centroid . Prove that
GA2 + GB2 + GC2 = `1/3` (AB2 + BC2 + CA2)
The centre of a circle is (−4, 2). If one end of the diameter of the circle is (−3, 7) then find the other end
The points A(−3, 6), B(0, 7) and C(1, 9) are the mid-points of the sides DE, EF and FD of a triangle DEF. Show that the quadrilateral ABCD is a parallelogram.
Find the coordinates of point P where P is the midpoint of a line segment AB with A(–4, 2) and B(6, 2).
Solution :
Suppose, (–4, 2) = (x1, y1) and (6, 2) = (x2, y2) and co-ordinates of P are (x, y).
∴ According to the midpoint theorem,
x = `(x_1 + x_2)/2 = (square + 6)/2 = square/2 = square`
y = `(y_1 + y_2)/2 = (2 + square)/2 = 4/2 = square`
∴ Co-ordinates of midpoint P are `square`.
